A366767 - OEIS

A366767

Array read by antidiagonals, where each row is the counting sequence of a certain type of fixed polyominoids.

1, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 0, 2, 2, 0, 1, 0, 2, 4, 2, 0, 1, 0, 2, 12, 6, 1, 0, 1, 0, 2, 38, 22, 0, 1, 0, 1, 0, 2, 126, 88, 0, 2, 1, 0, 1, 0, 2, 432, 372, 0, 6, 2, 1, 0, 1, 0, 2, 1520, 1628, 0, 19, 6, 4, 3, 0, 1, 0, 2, 5450, 7312, 0, 63, 19, 20, 0, 3

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

See A366766 (corresponding array for free polyominoids) for details.

LINKS

Table of n, a(n) for n=1..78.

Pontus von Brömssen, Python programs that relate row numbers and parameter sets.

Wikipedia, Polyominoid.

Index entries for sequences related to polyominoes.

EXAMPLE

Array begins:

n\k| 1 2 3 4 5 6 7 8 9 10 11 12

---+--------------------------------------------------------------------

1 | 1 0 0 0 0 0 0 0 0 0 0 0

2 | 1 1 1 1 1 1 1 1 1 1 1 1

3 | 2 0 0 0 0 0 0 0 0 0 0 0

4 | 2 2 2 2 2 2 2 2 2 2 2 2

5 | 2 4 12 38 126 432 1520 5450 19820 72892 270536 1011722

6 | 2 6 22 88 372 1628 7312 33466 155446 730534 3466170 16576874

7 | 1 0 0 0 0 0 0 0 0 0 0 0

8 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861

9 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861

10 | 1 4 20 110 638 3832 23592 147941 940982 6053180 39299408 257105146

11 | 3 0 0 0 0 0 0 0 0 0 0 0

12 | 3 3 3 3 3 3 3 3 3 3 3 3

CROSSREFS

Cf. A366766 (free), A366768.

The following table lists some sequences that are rows of the array, together with the corresponding values of D, d, and C (see A366766). Some sequences occur in more than one row. Notation used in the table:

X: Allowed connection.

-: Not allowed connection (but may occur "by accident" as long as it is not needed for connectedness).

.: Not applicable for (D,d) in this row.

!: d < D and all connections have h = 0, so these polyominoids live in d < D dimensions only.

*: Whether a connection of type (g,h) is allowed or not is independent of h.

| | | connections |

| | | g:112223 |

n | D | d | h:010120 | sequence

----+---+---+-------------+----------

1 | 1 | 1 | * -..... | A063524

2 | 1 | 1 | * X..... | A000012

3 |!2 | 1 | * --.... | 2*A063524

4 |!2 | 1 | X-.... | 2*A000012

5 | 2 | 1 | -X.... | 2*A001168

6 | 2 | 1 | * XX.... | A096267

7 | 2 | 2 | * -.-... | A063524

8 | 2 | 2 | * X.-... | A001168

9 | 2 | 2 | * -.X... | A001168

10 | 2 | 2 | * X.X... | A006770

11 |!3 | 1 | * --.... | 3*A063524

12 |!3 | 1 | X-.... | 3*A000012

13 | 3 | 1 | -X.... | A365655

14 | 3 | 1 | * XX.... | A365560

15 |!3 | 2 | * ----.. | 3*A063524

16 |!3 | 2 | X---.. | 3*A001168

17 | 3 | 2 | -X--.. | A365655

18 | 3 | 2 | * XX--.. | A075678

19 |!3 | 2 | --X-.. | 3*A001168

20 |!3 | 2 | X-X-.. | 3*A006770

21 | 3 | 2 | -XX-.. | A365996

22 | 3 | 2 | XXX-.. | A365998

23 | 3 | 2 | ---X.. | A366000

24 | 3 | 2 | X--X.. | A366002

25 | 3 | 2 | -X-X.. | A366004

26 | 3 | 2 | XX-X.. | A366006

27 | 3 | 2 | * --XX.. | A365653

28 | 3 | 2 | X-XX.. | A366008

29 | 3 | 2 | -XXX.. | A366010

30 | 3 | 2 | * XXXX.. | A365651

31 | 3 | 3 | * -.-..- | A063524

32 | 3 | 3 | * X.-..- | A001931

33 | 3 | 3 | * -.X..- | A039742

34 | 3 | 3 | * X.X..- |

35 | 3 | 3 | * -.-..X | A039741

36 | 3 | 3 | * X.-..X |

37 | 3 | 3 | * -.X..X |

38 | 3 | 3 | * X.X..X |

39 |!4 | 1 | * --.... | 4*A063524

40 |!4 | 1 | X-.... | 4*A000012

41 | 4 | 1 | -X.... | A366341

42 | 4 | 1 | * XX.... | A365562

43 |!4 | 2 | * -----. | 6*A063524

44 |!4 | 2 | X----. | 6*A001168

45 | 4 | 2 | -X---. | A366339

46 | 4 | 2 | * XX---. | A366335

47 |!4 | 2 | --X--. | 6*A001168

48 |!4 | 2 | X-X--. | 6*A006770

Sequence in context: A357860 A147648 A363879 * A113686 A361414 A193403

Adjacent sequences: A366764 A366765 A366766 * A366768 A366769 A366770

KEYWORD

nonn,tabl

AUTHOR

Pontus von Brömssen, Oct 22 2023

STATUS

approved